Because of spontaneous symmetry breaking and a mass gap, Dirac spectra
show universal behavior that can be understood by means of random matrix
theory. We discuss the effect of a nonzero lattice spacing on QCD
Dirac spectra and find tail states that have been observed before
in disordered condensed matter systems. Despite the Coleman-Mermin-Wagner
theorem Dirac spectra also show universal behavior in two dimensions,
but the unversality classes are different from those in four dimensions
and depend on the parity of the lattice. A complete classification
of two dimensional lattice QCD Dirac spectra in terms of the ten fold
classification of random matrix theories is given.